The '''totient''' function is also known as:
::* Euler's totient function
::* Euler's phi totient function
::* phi totient function
::* Φ function (uppercase Greek phi)
::* φ function (lowercase Greek phi)
;Definitions (as per number theory):
The totient function:
::* counts the integers up to a given positive integer '''n''' that are relatively prime to '''n'''
::* counts the integers '''k''' in the range '''1 ≤ k ≤ n''' for which the greatest common divisor '''gcd(n,k)''' is equal to '''1'''
::* counts numbers '''≤ n''' and prime to '''n'''
If the totient number (for '''N''') is one less than '''N''', then '''N''' is prime.
;Task:
Create a '''totient''' function and:
::* Find and display (1 per line) for the 1st '''25''' integers:
::::* the integer (the index)
::::* the totient number for that integer
::::* indicate if that integer is prime
::* Find and display the ''count'' of the primes up to 100
::* Find and display the ''count'' of the primes up to 1,000
::* Find and display the ''count'' of the primes up to 10,000
::* Find and display the ''count'' of the primes up to 100,000 (optional)
Show all output here.
;Related task:
::* [[Perfect totient numbers]]
;Also see:
::* [[wp:Euler's_totient_function|Wikipedia: Euler's totient function]].
::* [http://mathworld.wolfram.com/TotientFunction.html MathWorld: totient function].
::* [[oeis:/A000010|OEIS: Euler totient function phi(n)]].